TSTP Solution File: GEO062-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO062-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 64
% Syntax : Number of formulae : 158 ( 60 unt; 9 typ; 0 def)
% Number of atoms : 485 ( 123 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 578 ( 261 ~; 254 |; 0 &)
% ( 63 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 4 >; 11 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 467 ( 420 !; 0 ?; 467 :)
% Comments :
%------------------------------------------------------------------------------
tff(equidistant_type,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(w_type,type,
w: $i ).
tff(u_type,type,
u: $i ).
tff(lower_dimension_point_2_type,type,
lower_dimension_point_2: $i ).
tff(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
tff(insertion_type,type,
insertion: ( $i * $i * $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(
( between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2))
<=> between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2))
<=> ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2))
<=> ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_3) ).
tff(5,plain,
! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2))
| between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ between(U,V,W)
| between(W,V,U) )
<=> ( ~ between(U,V,W)
| between(W,V,U) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
tff(14,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(w,u,extension(w,u,lower_dimension_point_1,lower_dimension_point_2))
| between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
( ( u = extension(w,u,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u ) ),
inference(commutativity,[status(thm)],]) ).
tff(22,plain,
( ( u != extension(w,u,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) != u ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
^ [V: $i,U: $i] :
refl(
( ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
<=> ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
tff(27,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [V: $i,U: $i] : ( V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) )
| ( u != extension(w,u,lower_dimension_point_1,lower_dimension_point_2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
u != extension(w,u,lower_dimension_point_1,lower_dimension_point_2),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
extension(w,u,lower_dimension_point_1,lower_dimension_point_2) != u,
inference(modus_ponens,[status(thm)],[31,22]) ).
tff(33,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(
( ( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) )
<=> ( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| ( U = V )
| ( W = extension(U,V,V,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
tff(39,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ( U = V )
| ~ between(U,V,W)
| ( W = extension(U,V,V,W) ) )
| ( extension(w,u,lower_dimension_point_1,lower_dimension_point_2) = u )
| ~ between(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,w)
| ( w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
w = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),
inference(unit_resolution,[status(thm)],[45,42,32,20]) ).
tff(47,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w) = w,
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [V: $i,W1: $i,U: $i,U1: $i] :
refl(
( ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
<=> ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-3.ax',insertion) ).
tff(52,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [V: $i,W1: $i,U: $i,U1: $i] : ( insertion(U1,W1,U,V) = extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V) )
| ( insertion(u,w,u,v) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
insertion(u,w,u,v) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v) = insertion(u,w,u,v),
inference(monotonicity,[status(thm)],[47]) ).
tff(58,plain,
insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),
inference(transitivity,[status(thm)],[57,56]) ).
tff(59,plain,
( equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
<=> equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w) ),
inference(monotonicity,[status(thm)],[47,58,47]) ).
tff(60,plain,
( equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w)
<=> equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ~ equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w)
<=> ~ equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) = insertion(u,w,u,v),
inference(symmetry,[status(thm)],[56]) ).
tff(63,plain,
( ( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) )
<=> ( v = insertion(u,w,u,v) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( v = insertion(u,w,u,v) )
<=> ( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) ) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ( v != insertion(u,w,u,v) )
<=> ( v != extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( v != insertion(u,w,u,v) )
<=> ( v != insertion(u,w,u,v) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
v != insertion(u,w,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_equals_insertion) ).
tff(68,plain,
v != insertion(u,w,u,v),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
v != extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
( equidistant(u,v,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v))
<=> equidistant(u,v,u,insertion(u,w,u,v)) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(71,plain,
( equidistant(u,v,u,insertion(u,w,u,v))
<=> equidistant(u,v,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
^ [V: $i,W1: $i,U: $i,U1: $i] :
refl(
( equidistant(U,V,U1,insertion(U1,W1,U,V))
<=> equidistant(U,V,U1,insertion(U1,W1,U,V)) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V))
<=> ! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V)) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V))
<=> ! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i2_1) ).
tff(76,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V)),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V)),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V)),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
( ~ ! [V: $i,W1: $i,U: $i,U1: $i] : equidistant(U,V,U1,insertion(U1,W1,U,V))
| equidistant(u,v,u,insertion(u,w,u,v)) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
equidistant(u,v,u,insertion(u,w,u,v)),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
equidistant(u,v,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)),
inference(modus_ponens,[status(thm)],[80,71]) ).
tff(82,plain,
( between(u,v,w)
<=> between(u,v,w) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
tff(84,plain,
between(u,v,w),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ between(U,V,W)
| between(W,V,U) )
| ~ between(u,v,w)
| between(w,v,u) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
between(w,v,u),
inference(unit_resolution,[status(thm)],[87,16,84]) ).
tff(89,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) )
<=> ( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ between(U,V,W)
| ~ equidistant(U,V,U,X)
| ~ equidistant(W,V,W,X) )
<=> ( ~ between(U,V,W)
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ) )),
( ( ~ between(U,V,W)
| ~ equidistant(U,V,U,X)
| ~ equidistant(W,V,W,X)
| ( V = X ) )
<=> ( ~ between(U,V,W)
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X)
| ( V = X ) ) )),
rewrite(
( ( ~ between(U,V,W)
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X)
| ( V = X ) )
<=> ( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ) )),
( ( ~ between(U,V,W)
| ~ equidistant(U,V,U,X)
| ~ equidistant(W,V,W,X)
| ( V = X ) )
<=> ( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,V,U,X)
| ~ equidistant(W,V,W,X)
| ( V = X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,V,U,X)
| ~ equidistant(W,V,W,X)
| ( V = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15) ).
tff(95,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) )
| ~ between(w,v,u)
| ( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) )
| ~ equidistant(u,v,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v))
| ~ equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) )
| ~ between(w,v,u)
| ( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) )
| ~ equidistant(u,v,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v))
| ~ equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) )
| ~ between(w,v,u)
| ( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) )
| ~ equidistant(u,v,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v))
| ~ equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ between(U,V,W)
| ( V = X )
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X) )
| ~ between(w,v,u)
| ( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) )
| ~ equidistant(u,v,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v))
| ~ equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ( v = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v) )
| ~ equidistant(u,v,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v))
| ~ equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ),
inference(unit_resolution,[status(thm)],[101,98,88]) ).
tff(103,plain,
~ equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)),
inference(unit_resolution,[status(thm)],[102,81,69]) ).
tff(104,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
<=> ( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
tff(108,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w)
| equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w)
| equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w)
| equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) )
| ~ equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w)
| equidistant(w,v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v)) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
~ equidistant(v,w,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,v),w),
inference(unit_resolution,[status(thm)],[113,110,103]) ).
tff(115,plain,
~ equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)),
inference(modus_ponens,[status(thm)],[114,61]) ).
tff(116,plain,
( between(u,v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
<=> between(u,v,w) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(117,plain,
( between(u,v,w)
<=> between(u,v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
between(u,v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)),
inference(modus_ponens,[status(thm)],[84,117]) ).
tff(119,plain,
( equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
<=> equidistant(u,w,u,w) ),
inference(monotonicity,[status(thm)],[47,47]) ).
tff(120,plain,
( equidistant(u,w,u,w)
<=> equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) = extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),
inference(monotonicity,[status(thm)],[47]) ).
tff(122,plain,
extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) = w,
inference(transitivity,[status(thm)],[121,47]) ).
tff(123,plain,
( equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
<=> equidistant(u,w,u,w) ),
inference(monotonicity,[status(thm)],[122,47]) ).
tff(124,plain,
( equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
<=> equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(transitivity,[status(thm)],[123,120]) ).
tff(125,plain,
^ [W: $i,V: $i,Y: $i,X: $i] :
refl(
( equidistant(Y,extension(X,Y,W,V),W,V)
<=> equidistant(Y,extension(X,Y,W,V),W,V) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
<=> ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
<=> ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V) ),
inference(rewrite,[status(thm)],]) ).
tff(128,axiom,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
tff(129,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
( ~ ! [W: $i,V: $i,Y: $i,X: $i] : equidistant(Y,extension(X,Y,W,V),W,V)
| equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)),
inference(unit_resolution,[status(thm)],[132,131]) ).
tff(134,plain,
equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)),
inference(modus_ponens,[status(thm)],[133,124]) ).
tff(135,plain,
^ [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
refl(
( ( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
<=> ( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
<=> ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
<=> ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
^ [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
rewrite(
( ( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
<=> ( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ) )),
inference(bind,[status(th)],]) ).
tff(139,plain,
( ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
<=> ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,axiom,
! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i2_3) ).
tff(141,plain,
! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) ),
inference(modus_ponens,[status(thm)],[143,136]) ).
tff(145,plain,
( ( ~ ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
| ~ between(u,v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| ~ equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) )
<=> ( ~ ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
| ~ between(u,v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| ~ equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ~ ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
| ~ between(u,v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| ~ equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
( ~ ! [W: $i,V: $i,W1: $i,U: $i,U1: $i] :
( ~ between(U,V,W)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,insertion(U1,W1,U,V),W1) )
| ~ between(u,v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| ~ equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
( ~ between(u,v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| ~ equidistant(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w))
| equidistant(v,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),insertion(u,extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w),u,v),extension(extension(w,u,lower_dimension_point_1,lower_dimension_point_2),u,u,w)) ),
inference(unit_resolution,[status(thm)],[147,144]) ).
tff(149,plain,
$false,
inference(unit_resolution,[status(thm)],[148,134,118,115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO062-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 05:13:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------